Answer:
Part A
There is sufficient statistical evidence to suggest that the difference between the proportion of White students exposed to poverty is likely due to something beside chance
Part B
There is sufficient statistical evidence to suggest that the difference between the proportion of Black students exposed to poverty is likely due to something beside chance
Explanation:
Part A
The given data are;
The percent of White students exposed to school poverty in 2,000,
= 30%
The number of White students in the district in 2,000, n₁ = 5184
The percent of White students exposed to school poverty in 2,015,
= 47.8%
The number of White students in the district in 2,015, n₂ = 7,306
The significant level, α = 0.05
The confidence level = 1 - α/2 = 1 - 0.05/2 = 0.975
The critical z at 0.975 confidence level,
= 1.96
The null hypothesis, H₀;
=
The null hypothesis, H₀;
≠
The Z test is given as follows;
Therefore, we have;
Given that the actual Z is much larger than the critical Z, we reject the null hypothesis that the difference between the proportion of White students is likely due to something other than chance
Part B, we have;
The percent of black students exposed to school poverty in 2,000,
= 34.5%
The number of black students in the district in 2,000, n₁ = 1035
The percent of black students in the district in 2,015,
= 76.1%
The number of black students in the district in 2,000, n₁ = 2037
Similarly, due to the large value of Z compared to
, there must be other variables responsible for the difference in proportion